Journal of Spectroscopy

Volume 2018, Article ID 5392658, 8 pages

https://doi.org/10.1155/2018/5392658

## Semiempirical Efficiency Calibration in Semiconductor HPGe Gamma-Ray Spectroscopy

Institute of Nuclear Sciences “Vinča”, University of Belgrade, Mike Petrovica Alasa 12-16, 11001 Belgrade, Serbia

Correspondence should be addressed to Ivana Vukanac; sr.acniv@canakuv

Received 30 January 2018; Revised 21 March 2018; Accepted 16 April 2018; Published 10 May 2018

Academic Editor: Eugen Culea

Copyright © 2018 Jelena Krneta Nikolić et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

One of the main problems in quantitative gamma-ray spectroscopy is the determination of detection efficiency, for different energies, source-detector geometries, and composition of samples or sources. There are, in principle, three approaches to this issue: experimental, numerical, and semiempirical. Semiempirical approach is based on the calculation of the efficiency for the measured sample on the basis of an experimental efficiency measured on the same detector, but with a calibration source that can be of different size, geometry, density, or composition—the so-called efficiency transfer. The aim of this paper is to analyze the semiempirical approach, using EFFTRAN and MEFFTRAN software as a typical example. These software were used in the Department of Radiation and Environmental Protection, Vinča Institute of Nuclear Sciences, on three HPGe detectors. The results were compared to the experimentally obtained efficiency, and further validation is performed by measuring reference materials issued within the framework of several interlaboratory intercomparisons. The analysis of the results showed that the efficiency transfer produces good results with the discrepancies within the limits of the measurement uncertainty. Also, for intercomparison measurement, *u*_{test} criterion for the trueness of the result was applied showing that the majority of the obtained results were acceptable. Some difficulties were identified, and the ways to overcome them were discussed.

#### 1. Introduction

Gamma spectrometry is a widely used method for the measurement of gamma-ray emitting radionuclide content in various materials. It is a method of choice for the measurement of environmental samples conducted, for example, during radiological monitoring of the environment and contamination control. This method is based on the interaction of gamma rays emitted from the source and the active volume of the detector. Semiconductor detectors and among them, high-purity germanium (HPGe) detectors, are proven to be very sensitive and have good energy and time resolution. That is why this type of detector is commonly used for gamma-spectroscopic measurements.

In the absence of background, the result of any gamma-spectroscopic measurement is represented by the spectrum of photons originating from the source that are collected by the multichannel analyzer (MCA) with the number of detected photons in a peak at a specific energy being proportional to the activity of the given radionuclide. One of the main problems in quantitative gamma-ray spectroscopy is the determination of detection efficiency, for different energies, different source-detector geometries, and different compositions of voluminous samples or sources. This task represents the efficiency calibration of the detector.

The quality of the results of gamma-spectrometric measurements is dependent on the knowledge of detector efficiency for different sample geometries, chemical compositions, and sample-detector geometries. In reality, measurement depends on the geometry, structure, and the chemical composition of the sample, and the efficiency calibration for each specific case is not always available. That is why several methods for efficiency calibration were developed. There are, in principle, three approaches to this issue: experimental, numerical, and semiempirical. These methods vary in difficulty, reliability of the obtained results, time and resources required, and so on.

Experimental approach utilizes standardized sources (calibration sources) with composition, density, and geometry that are as close as possible to the measured samples. The direct measurement of different calibration sources containing *γ*-ray emitters within the energy range of interest, and their subsequent fitting to a parametric function, yields the best results. However, this approach requires a large number of calibration sources, implying a high financial cost, a long counting time, and complicated and time-consuming preparation of the calibration sources. This problem is especially pronounced when environmental samples are of interest due to their diversity in composition and structure [1].

Numerical methods of the efficiency calibration consist of a computer simulation of the processes that contribute to the detection of the emitted photons. Monte Carlo simulation, such as GEANT4, MCNP, EGS, and PENELOPE, can be adapted to the computation of the efficiency of gamma-ray spectrometry detectors [2]. Dedicated codes, such as GESPECOR, LABSOCS, ANGLE, and so on, are specifically tailored to solve most of the problems concerning gamma-spectrometric measurements [3]. Monte Carlo simulation codes are developed to simulate the response of complex particle detectors and for variety of different high energy and nuclear interactions [4]. In case of gamma spectrometry, these codes need defining appropriate processes for interaction of gamma photons with the detector and the corresponding database used in the development of the application for the particular detector, which may be time-consuming and may require proficiency in programming language [5]. Once an application is developed, the use is relatively easy and the results are straightforward. Besides these software packages that simulate detector response to gamma rays, there is also numerical method (“direct matrices multiplication” (DMM) method) based only on general decay scheme developed to determine peak efficiencies as well as the activity of the source [6, 7].

The third approach to the efficiency calibration is the semiempirical approach. It is based on the calculation of the efficiency for the measured sample on the basis of an experimental efficiency curve obtained for the same detector, but with a calibration source that can be of different sizes, geometries, densities, or compositions—the so-called efficiency transfer. The procedure saves time and resources, since sample-specific experimental calibration is avoided. It has been proven especially useful in environmental measurements [8], where an ultimate precision in calibration is usually not required and a variety of different sources might be measured. Many software packages were developed in order to perform efficiency transfer calculations with a known set of parameters. Some are EFFTRAN, MEFFTRAN, ETNA, ANGLE, and so on. The result of the calculation is transfer coefficient, which is the ratio of the efficiency for unknown sample and reference efficiency.

The aim of this paper is to analyze the semiempirical approach to the efficiency calibration of the HPGe detector. A specific example of the efficiency transfer software will be analyzed in more detail, with practical instruction, and advantages and drawbacks pointed out. The results of the testing of this method will also be presented.

##### 1.1. Semiempirical Efficiency Calibration: EFFTRAN and MEFFTRAN

Semiempirical methods for detector efficiency calculation are based on the assumption that the detector efficiency for the measured sample can be calculated knowing the reference efficiency obtained by measuring the calibration source with known composition and activity. This is referred to as “efficiency transfer.” The relation between reference efficiency and efficiency for the measured sample is defined in (1), according to the model proposed by Moens et al. [9]:where represents the unknown efficiency, is the reference efficiency, is the effective solid angle for the given measurement configuration, and is the effective solid angle for reference configuration. The effective solid angle depends on the geometry of the detector, the source–detector position, and needs to be calculated. Both and depend on the gamma photon energy and, through the interaction probabilities, on the chemical composition of the crystal and source.

In order to calculate these effective solid angles, some sort of software is needed for solving the partial differential equations. Often in the calculation, Monte Carlo integration is used as a suitable choice for many-dimensional systems. This calculation requires relatively precise information on geometry of the detector (crystal geometry, housing geometry and composition, active and inactive layers, etc). Also, the information on both calibration source and measured sample has to be provided (diameter, filling height, matrix composition, thickness of the container, etc.). Because the model of the sample, as well as the detector crystal, can be constructed from cylinders only, the only complex operation required in the code is the calculation of the path length traversed through the cylinders defining the counting geometry by a gamma-ray originating at an arbitrary location [10].

The procedure for obtaining the unknown efficiency is as follows. Firstly, a calibration source with known composition and activity is measured, and the detection efficiency has to be calculated for all energies emitted from the source using the following equation:where is the number of detected gamma photons, is the coincidence summing correction factor, is the measurement time, is the emission probability at given energy , and is the activity of the radionuclide present in the calibration source.

As with all measurement, also in this case, a measurement uncertainty has to be defined. It is expressed as a combined standard uncertainty using the following equation:where is the relative uncertainty of the activity of the radionuclide present in the calibration source (1-2%), is the relative statistical uncertainty, and includes all other contributions to the uncertainty such as measurement of the reference material mass, the uncertainty of the positioning of the sample on the detector, measurement time uncertainty, and radioactive decay during measurement, and so on, which are estimated to be 2%. Finally, is the uncertainty of the coincidence correction factor (≈1.2%).

Then, the geometrical characteristics of the detector need to be defined. Due to the specific shape of the detector crystal and surrounding material, the geometry of the detector can be defined as a set of cylinders with a certain radius and height, made of known material. These data are usually available from the manufacturer of the detector itself. Furthermore, the reference source and measured sample characteristics are defined, also as a set of cylinders. The material of both calibration source and sample is defined using its chemical formulae, the percent of each compound in the total mass of the source or sample, and the density of the matrix. After all these data are entered, the calculation gives the transfer coefficients which, when multiplied with the reference efficiency obtained by measuring the calibration source, yield the unknown efficiency for the measured sample.

As a typical example of efficiency transfer software, here we will use EFFTRAN and MEFFTRAN software. EFFTRAN, an efficiency transfer software, is dedicated to calculation of efficiency transfer for cylindrical samples, while MEFFTRAN performs the same calculations for the Marinelli beaker [10, 11]. The software is organized as a Microsoft excel file with three modules. There is a module for defining the material of the calibration source and measured sample (Material), a module for calculation of the efficiency transfer (Efficiency Transfer), and a module for calculation of coincidence correction factors (Coincidence Correction). In the module Efficiency Transfer, the geometrical characteristic of the detector crystal has to be defined. This means that also, the material of the crystal and detector window should be defined, as well as the thickness of the dead layers and window to crystal gap.

All the data that are required are not always known and cannot be precisely defined, thus contributing to the measurement uncertainty. However, the lack of precision and uncertainties rising from poor knowledge of the composition of the sample cannot be avoided.

The combined relative uncertainty of the efficiency obtained by MEFFTRAN or EFFTRAN can estimated according to the following expression:where is the relative uncertainty of the reference efficiency value, defined in (2), is the uncertainty of the transfer factors calculated by the program as a statistical uncertainty of the Monte Carlo integration (≈1.2%), is the uncertainty associated with the geometry of the detector, and is the uncertainty associated with the characteristics of the sample. As it can be seen from (4), the parameters contributing to the uncertainty are combined as independent variables.

The uncertainty of the parameters of the detector geometry can be estimated by varying each parameter and calculating the amount of change it produces on the transfer factors. In this way, the uncertainty can be estimated to be around 1% for crystal diameter and length, and crystal cavity diameter and length. According to this estimation, the contribution can be obtained by combining these uncertainties as a square root of sum of squares [5].

The characteristics of the calibration source and measured samples also contribute to the measurement uncertainty via parameter .

In the case of EFFTRAN, the density of the samples was calculated by dividing the measured mass of the sample with the volume of the sample. Therefore, the contribution of the density to the uncertainty parameters is the combined uncertainty of mass and volume (1-2%). The chemical composition of the container can be well defined, but for the sample, the situation is more complicated, and poor knowledge of the chemical composition can be the source of larger uncertainty.

The definition of the chemical composition of the material can significantly contribute to the uncertainty budget. In order to define this contribution, an in-depth analysis has to be performed. This will be the subject of the investigation that is under way. One simple way to estimate this contribution is to vary the composition of the sample by adding or omitting some elements or compounds. Of course, this does not apply to the samples with known composition such as water and charcoal. In case of soil and grass, we have varied the composition in order to see how these changes reflect on the result of the efficiency transfer. It has been determined that omitting Fe from the composition of the soil leads to changes in the result that are around 2% for both EFFTRAN and MEFFTRAN, while changing the content of C leads to the changes in the results that span from 1% in case of EFFTRAN to 8% in case of MEFFTRAN. Much larger changes are observed in case of grass composition, namely, the change of C content with respect to the cellulose content. These changes ranged from 7 to 29%, with the largest influence noticed for the lowest energy. It is noticed that the influence of the composition lowers with the rising energy. Also, in some cases, such as grass, the influence of the chemical composition can be larger than the influence of the sample thickness. How these changes combine with each other (can one simply sum or multiply all changes) is yet to be analyzed. For the sake of simplicity in this paper, the contribution to the uncertainty arising from the chemical composition definition is estimated to be 10% average, for all energies.

In the case of MEFFTRAN, since all samples were Marinelli beakers, the only variable parameters of the sample geometry are sample filling height and mass. The contribution of 0.8% for the sample filling height was included in the uncertainty budget. This contribution was calculated by conducting the efficiency transfer for 5 different filling heights (105 mm, 100 mm, 95 mm, 90 mm, and 85 mm) and calculating the ratio between the different transfer coefficients. It is then established that the 1% change in height leads to 0.8% change in transfer coefficients, thus contributing to the with 0.8%. The uncertainty of the sample mass is estimated to be 1%. Since the software requires the density of the matrix to be defined, these two were combined to produce the square of the sample density uncertainty equal to 1.64%. The contributions and are the same as in the case of EFFTRAN.

The uncertainty budget is presented in Table 1.